ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of KNbSe2 (Materials Project id mp-7940)

       108       35       28        0        0        0  
        35      108       28        0        0        0  
        28       28      119        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.444 GPaEV = 89.884 GPaGV = 36.267 GPaνV = 0.23921
ReussKR = 57.431 GPaER = 88.755 GPaGR = 35.718 GPaνR = 0.24243
HillKH = 57.438 GPaEH = 89.32 GPaGH = 35.992 GPaνH = 0.24082

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 36 GPa 73 GPa 89.624 GPa 172.38 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 83.35 GPa 108.03 GPa 5.6314 TPa–1 5.8903 TPa–1 32 GPa 42.406 GPa0.167880.31434Value
Anisotropy 1.296 1.0460 1.325 1.8724Anisotropy
Axis -0.5484
0.5485
0.6312
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.7071
-0.0000
0.6759
0.0001
-0.7370
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
0.0000
-1.0000
-0.7370
-0.0002
-0.6759
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane